Consider a circular roller coaster loop of radius 11 m. You already know that if

Question

Consider a circular roller coaster loop of radius 11 m. You already know that if the car starts from a height of 2.5 r at rest, the normal force acting on the car at the top will vanish.


Now assume the car starts from a level track, a height of 11 m above the ground. The track first guides the car to ground level and then into the loop. At which initial speed must the car move on the elevated track (height 11 m) such that it still has the required speed at the top of the loop for the normal force to vanish?

Explanation / Answer

From principle of conservation of energy:

Total mechanical energy at the lower point of loop = total mechanical energy at the highest point of loop

1/2* m*Vl2 = 1/2* m*vH2 + mgH                           ( K.E = 1/2* m* V2 ,      P.E = mgH)

since att highest point V = 0 ( because it starting from rest )

Vl = ( 2gH )1/2

Vl = ( 2*10*11)1/2 = 14.8 m/s     ( this is the speed with the car should enter in the loop)

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